Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism
Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism
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DOI：
10.1063/1.4935490
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发表时间：
2015-12-28
影响因子：
4.4
通讯作者：
Karniadakis, George Em
中科院分区：
文献类型：
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作者：
Li, Zhen;Bian, Xin;Karniadakis, George Em
用于粗粒化复杂动力系统的Mori-Zwanzig形式主义通常引入记忆效应。马尔可夫假设的三角洲相关的波动力经常被用来简化制定粗粒度（CG）模型和数值实现。然而，当一个系统的时间尺度没有明确分离时，记忆效应变得很强，马尔可夫假设变得不准确。为此，我们将记忆效应纳入CG建模通过保留CG变量之间的非马尔可夫相互作用，和记忆内核直接从微观动力学进行评估。对于一个具体的例子，分子动力学（MD）模拟的星星聚合物熔体进行，而相应的CG系统被定义为分组成单个集群的许多键合原子。然后，从MD模拟中获得CG簇之间的有效相互作用以及记忆核。构造的具有记忆核的CG力场导致非马尔可夫耗散粒子动力学（NM-DPD）。马尔可夫近似和非马尔可夫近似的CG模型之间的定量比较表明，包括记忆效应使用NM-DPD产生类似的结果，基于马尔可夫的DPD，如果系统具有明确的时间尺度分离。然而，对于时间尺度分离较小的系统，NM-DPD可以再现与系统如何响应高频干扰有关的正确的短时特性，这是基于马尔可夫的DPD模型无法捕获的。(C)2015年AIP Publishing LLC。
The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model. (C) 2015 AIP Publishing LLC.